410edo: Difference between revisions

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== Theory ==

410edo is closely related to [[205edo]], but the [[patent val]] differs on the mappings for 7 and 13. It is [[contorted]] in the [[5-limit]], tempering out 1600000/1594323 ([[amity comma]]) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo| -29 -11 20 }} (gammic comma) and {{monzo| 47 -15 -10 }} (~~qintosec~~ comma). It tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.

410edo is closely related to [[205edo]], but the [[patent val]] differs on the mappings for 7 and 13. It is [[contorted]] in the [[5-limit]], tempering out 1600000/1594323 ([[amity comma]]) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo| -29 -11 20 }} (gammic comma) and {{monzo| 47 -15 -10 }} (quintosec comma). It tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.

410edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] ~~temperament~~, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.

410edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] temperaments, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.

410edo works much better as a no-11 no-13 subgroup temperament, with a sharp tendency to harmonics up to 29. For example, it tempers out [[1216/1215]], [[1225/1224]], [[1445/1444]], and 2500/2499 in the 2.3.5.7.17.19 subgroup.

410edo works much better as a no-11 no-13 subgroup temperament, with a sharp tendency to harmonics up to 29. For example, it tempers out [[1216/1215]], [[1225/1224]], [[1445/1444]], and [[2500/2499]] in the 2.3.5.7.17.19 subgroup.

=== Prime harmonics ===

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== Music ==

* [https://www.youtube.com/watch?v=-bm5UdmveZU All Time Best] - decoid[40], cover of [[Phlub]] by [[Eliora]]

* [https://www.youtube.com/watch?v=-bm5UdmveZU ''All Time Best''] – decoid[40], cover of [[Phlub]] by [[Eliora]]

~~[[Category:Equal divisions of the octave|###]] ~~

[[Category:Semiluna]]

[[Category:Hemiluna]]

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 == Theory ==
-edo is closely related to [[205edo]], but the [[patent val]] differs on the mappings for 7 and 13. It is [[contorted]] in the [[5-limit]], tempering out 1600000/1594323 ([[amity comma]]) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo| -29 -11 20 }} (gammic comma) and {{monzo| 47 -15 -10 }} (qintosec comma). It tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.
+edo is closely related to [[205edo]], but the [[patent val]] differs on the mappings for 7 and 13. It is [[contorted]] in the [[5-limit]], tempering out 1600000/1594323 ([[amity comma]]) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo| -29 -11 20 }} (gammic comma) and {{monzo| 47 -15 -10 }} (quintosec comma). It tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.
-edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] temperament, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.
+edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] temperaments, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.
-edo works much better as a no-11 no-13 subgroup temperament, with a sharp tendency to harmonics up to 29. For example, it tempers out [[1216/1215]], [[1225/1224]], [[1445/1444]], and 2500/2499 in the 2.3.5.7.17.19 subgroup.
+edo works much better as a no-11 no-13 subgroup temperament, with a sharp tendency to harmonics up to 29. For example, it tempers out [[1216/1215]], [[1225/1224]], [[1445/1444]], and [[2500/2499]] in the 2.3.5.7.17.19 subgroup.
 === Prime harmonics ===
@@ Line 123: / Line 123: @@
 == Music ==
-* [https://www.youtube.com/watch?v=-bm5UdmveZU All Time Best] - decoid[40], cover of [[Phlub]] by [[Eliora]]
+* [https://www.youtube.com/watch?v=-bm5UdmveZU ''All Time Best''] – decoid[40], cover of [[Phlub]] by [[Eliora]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Semiluna]]
 [[Category:Hemiluna]]